Analysis of Factors Influencing the Understanding of the Concept of Infinity

Autor/inn/en	Kolar, Vida Manfreda; Cadez, Tatjana Hodnik
Titel	Analysis of Factors Influencing the Understanding of the Concept of Infinity
Quelle	In: Educational Studies in Mathematics, 80 (2012) 3, S.389-412 (24 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-011-9357-7
Schlagwörter	Educational Research; Foreign Countries; Mathematics Education; Mathematical Concepts; Children; Teachers; Preservice Teacher Education; Primary Education; Mathematics Instruction; Elementary School Mathematics; Teaching Methods; Task Analysis; Slovenia + Suchen Sie Ihr Suchwort? Bildungsforschung; Pädagogische Forschung; Ausland; Mathematische Bildung; Child; Kind; Kinder; Lehrer; Lehrerin; Lehrende; Lehramtsstudiengang; Lehrerausbildung; Primarbereich; Mathematics lessons; Mathematikunterricht; Elementare Mathematik; Schulmathematik; Teaching method; Lehrmethode; Unterrichtsmethode; Aufgabenanalyse; Slowenien
Abstract	The article discusses the understanding of infinity in children, teachers and primary teacher students. It focuses on a number of difficulties that people cope with when dealing with problems related to infinity such as its abstract nature, understanding of infinity as an ongoing process which never ends, understanding of infinity as a set of an infinite number of elements and understanding of well-known paradoxes. In the empirical section of the article, a study is described that was conducted at the Faculty of Education, University of Ljubljana, Slovenia. It encompassed 93 third-year students of the Primary Teacher Education study programme with the aim of researching their understanding of the concept of infinity. The focus was on finding out how primary teacher students who received no in-depth instruction on abstract mathematical content understand different types of infinity: infinitely large, infinitely many and infinitely close, what argumentation they provide for their answers to problems on infinity and what their basic misunderstandings about infinity are. The results show that the respondents' understanding of infinity depends on the type of the task and on the context of the task. The respondents' justifications for the solutions are based both on actual and on potential infinity. When solving tasks of the types "infinitely large" and "infinitely many", they provide justifications based on actual infinity. When solving tasks of the type "infinitely close", they use arguments based on potential infinity. We conclude that when they feel unsure of themselves, they resort to their primary method of dealing with infinity, that is, to potential infinity. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10